If the company followed their documented severance policy, what grounds would the OP have for a lawsuit? They didn't mention anything that the company did that might be grounds for suing them (e.g., discrimination, breach of contract, etc.). People get laid off all the time, and there's no legal requirement for a company to pay any severance at all (I'm assuming they're in the U.S.).

However, I don't see any downside in asking for more severance. The worst the company could do is say "no".